Interpolation and reinitialization in time-domain simulation of power electronic circuits

EMTP-type realization of model reduction algorithms for transient simulation of distribution networks

“…To deal with the switch actions in real simulation applications, the above procedure should also be coordinated with the interpolation algorithm [13], which varies in different programs.…”

On the Numerical Accuracy of Electromagnetic Transient Simulation With Power Electronics

“…However, the system for reinitialization can be solved more efficiently because the known variables x partition the system in small subproblems [15], [58]. In [19], a reinitialization technique is presented that does not require an additional solver. However, this method is only first-order accurate because it uses backward Euler and linear extrapolation.…”

“…Consequently, a sufficiently small step size is required to account for the lack of synchronization with events. To prevent this, several methods, including those of NETOMAC and PSCAD, employ linear interpolation to rollback the solution to the moment of switching before executing the corresponding switch actions [4], [14], [17], [19], [24], [25], [29]- [31], [53]- [57]. However, as the approximation error of linear interpolation is O(h 2 ), the local O(h 3 ) accuracy of the trapezoidal method is still not matched in the respective simulation steps.…”

“…To prevent additional errors due to delayed switch actions, a valid switch configuration must be found without advancing in time [15], [16], [19]. EMTP-RV, with the "Simultaneous Switching" option enabled, rejects exploratory steps until a valid switch configuration is found [42].…”

“…XTAP uses 2s-DIRK, an L-stable method of order two. The anticipated second-order accuracy of these methods is, however, compromised at switch events because approximations of lower order are involved, for instance due to the use of linear interpolation for event localization [17], due to the use of backward Euler (BE) steps for the suppression of numerical oscillations [18], or in the reinitialization process after switching [19]. Consequently, simulations with switch events are generally less accurate than simulations without J. Tant and J. Driesen are both with ELECTA, Department of Electrical Engineering, KU Leuven, Leuven, Belgium, and Energyville, Genk, Belgium (e-mail: jeroen.tant@esat.kuleuven.be; johan.driesen@esat.kuleuven.be).…”